Most methods for temporal pattern mining assume that time is represented by points in a straight line starting at some initial instant. Discovering sequential patterns in customer's transactions is a well-known application where such data mining methods have been used successfully. In this paper, we consider a new kind of temporal pattern where both interval and punctual time representation are considered. These patterns, which we call temporal point-interval patterns aim at capturing how events taking place during different time
periods or at different time instants relate to each other. The datasets where these kind of patterns may appear are temporal relational databases whose relations contain point or interval timestamps. We use a simple extension of Allen's Temporal Interval Logic as a formalism for specifying these temporal patterns. We also present the algorithm MILPRIT for mining temporal point-interval patterns, which uses variants of the classical level-wise search algorithms. Besides, MILPRIT allows a broad spectrum of constraints to be incorporated into the mining process. These constraints aim at restricting the search space (and so, improving the algorithm perfomance) as well as returning patterns closer to user interest. Finally, we present an extensive set of experiments of MILPRIT executed over synthetic and real data and analyse its results.